With me, Sivir has this annoying issue. Whenever she is
autoattacking minions and kills one, usually she stops
autoattacking even if the next minion is one step away from the
autoattack's range.

It's weird because I don't have this problem with Twisted Fate
(just an example). He normally approaches the minion and starts to
autoattack when it gets into the range. So, can anyone guess what
is up with her?

Sivir has only 25 less range than TF. I thought Sivir lacks
a sort of "vision" range, maybe? And that "vision" range allows a
champion to walk towards the next minion? I mean, since she usually
don't autowalk towards a minion, her "vision" range is maybe
broken, and has a value equal to her autoattack range.